{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This code does the piecewise interploation of degree 1 on an exponential function with two dependent variables in 2D space\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109c22390>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pUgCrVgHffivcO3nyGM+76/4uHHl8BJ79PW0noI1IlTwVfv3mV0w9OxUb225U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\nFoXdFMBN3t700SZfu8vSM2lAcnVRvf66u6PrnHjXeTTGJLu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kC+ueMiY4w4GdQM+wG2KM\nXyxpGBMAEekDfAPoD/yniFS3n4kxKceShjE+iyzZ/Tjww8ig+EPAtHBbZYw/LGkY47/JwA5VXR55\n/X9AtogMDrFNxvjC7p4yxhjjmV1pGGOM8cyShjHGGM8saRhjjPHMkoYxxhjPLGkYY4zxzJKGMcYY\nzyxpGGOM8cyShjHGGM/+H3GovvYwyCVwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1092dec10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "######Problem 2 \n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "%matplotlib inline\n",
    "\n",
    "# These are the simplied charact. lagrange polynomial, y2 represents l2 and so on.. \n",
    "\n",
    "plt.figure(1)\n",
    "def y2(x):\n",
    "    return 243./16*((x*x-1)*(x*x-4./9)*(x-1./3)*x)\n",
    "def y3(x):\n",
    "    return -81./4*((x*x-1)*(x*x-4./9)*(x*x-1./9))\n",
    "def y4(x):\n",
    "    return 243/16*((x*x-1)*(x*x-4./9)*(x+1./3)*x)\n",
    "\n",
    "x = np.arange(-1,1,0.001)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.plot(x,y2(x),'r',label='L2')\n",
    "plt.plot(x,y3(x),'b',label='L3')\n",
    "plt.plot(x,y4(x),'g',label='L4')\n",
    "plt.xlabel('X');plt.ylabel('Interpolated value')\n",
    "plt.title('Lagrange characteristic polynomials vs x ',fontsize=12,color='black')\n",
    "plt.legend( loc='upper right')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8DcRSufIg3n23p9OC1JGRHYiIqAlADEvoRArt6AHEsn793yVubej9jJxLSfen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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa187fffd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### Problem 3\n",
    "plt.figure(2)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "def f1(x):\n",
    "        return np.sin(2*np.pi*x)\n",
    "\n",
    "x = np.linspace(-1.0,1.0,200)\n",
    "x1 = np.linspace(-1,1,22)\n",
    "y1 = f1(x1)\n",
    "y_pert=np.array(22*[0.])\n",
    "import random\n",
    "for i in range(0,22):\n",
    "          pert= random.uniform(0,0.001)\n",
    "          y_pert[i] = y1[i]+ pert\n",
    "sum1=np.array(200*[0.])\n",
    "sum1_pert=np.array(200*[0.])\n",
    "#x2=np.array([-0.9, 0.9])\n",
    "for k in range(0,200):\n",
    "        M=np.array(22*[1.])\n",
    "        for i in range(0,22):\n",
    "                for j in range(0,22):\n",
    "                        if(j!=i):\n",
    "                                #if(x1[j]!=x2[k]):\n",
    "                                L= (x[k]-x1[j])/(x1[i]-x1[j])\n",
    "                                M[i] = M[i]*L\n",
    "#               print 'x2[k]=',x2[k], ' M[i]=',M[i], ' sum1[k]=',sum1[k]\n",
    "                sum1[k] = sum1[k]+M[i]*y1[i]\n",
    "                sum1_pert[k] = sum1_pert[k]+M[i]*y_pert[i]\n",
    "#print sum1[0], sum1[1], f1(-0.9), f1(0.9)\n",
    "plt.grid(True)\n",
    "plt.plot(x,f1(x),'bo',label='f(x)=sin(2*pi*x)')\n",
    "plt.plot(x,sum1,'k',label='interpolation')\n",
    "plt.plot(x,sum1_pert,'r',label='perturbation')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('graph of y=f(x) vs x ',fontsize=12,color='black')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y');\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#####################################################################################\n",
    "# this is a function which calculates charac. lagrange polynomial\n",
    "# for the refrence triangle\n",
    "#####################################################################################\n",
    "def lagr_tri(order,x,y):\n",
    "\tif order==0:\n",
    "\t\tl=1-x-y\n",
    "\telif order==1:\n",
    "\t\tl=x\n",
    "\telse:\n",
    "\t\tl=y\n",
    "\treturn l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#####################################################################################\n",
    "# this is a function which finds the global node id of the \n",
    "# local refrence triangle\n",
    "#####################################################################################\n",
    "def tri_connect(elem_id, loc_node):\n",
    "\tglobal m \n",
    "\tglobal n\n",
    "\t\n",
    "\tif elem_id<(n-1)*(n-1):\n",
    "\t\t#differ = elem_id - (n-1) \n",
    "\t\tindex= elem_id/ (n-1)\n",
    "\t\tif loc_node==0:\n",
    "\t\t\tglob_node= m[elem_id+index,:]\n",
    "\t\telif loc_node==1:\n",
    "\t\t\tglob_node=m[elem_id+1+index,:]\n",
    "\t\telse:\n",
    "\t\t\tglob_node=m[elem_id+n+index,:]\n",
    "\telse:\n",
    "\t\tdiffer = elem_id - (n-1) * (n-1) \n",
    "\t\tindex= differ/ (n-1)\n",
    "\t\t#index= ( elem_id - (n-1) * (n-1) )//(n-1)\n",
    "\t\tif loc_node==0:\n",
    "\t\t\tglob_node= m[index+differ+n+1,:]\n",
    "\t\telif loc_node==1:\n",
    "\t\t\tglob_node=m[index+differ+n,:]\n",
    "\t\telse:\n",
    "\t\t\tglob_node=m[index+differ+1,:]\t\n",
    "\treturn glob_node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#####################################################################################\n",
    "# This is a function which \n",
    "# Calculates the function value at the nodes provided\n",
    "#####################################################################################\n",
    "\n",
    "def calc_function(x,y):\n",
    "\tf= np.exp(-(x**2 +y**2) )\n",
    "\treturn f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m =  [-0.75 -0.75] [-1.   -0.75] [-0.75 -1.  ]\n",
      "[[-4. -0.]\n",
      " [-0. -4.]]\n",
      "1.0 0.939413062813 0.939413062813\n"
     ]
    }
   ],
   "source": [
    "#####################################################################################\n",
    "\n",
    "# This is the main program  \n",
    "# \n",
    "#####################################################################################\n",
    "\n",
    "\n",
    "# initializing some variables to be used later.\n",
    "global n # number of divisions in x or y axis\n",
    "n= 9\n",
    "x = np.linspace(-1,1,n)\n",
    "y=np.linspace(-1,1,n)\n",
    "\n",
    "global m # number of nodes\n",
    "m=np.zeros((81,2))\t\t\t# all nodes \n",
    "z=np.zeros((3,2))\t\t\t# triangle node points \n",
    "lag_glob=np.zeros((3))\t\t# lagrange charac. global polynomial function \n",
    "b=np.zeros((128,2))\t\t\t# b vector \n",
    "lagr_poly=np.zeros((128))    # global polynomial interpolated value\n",
    "inverse_func= np.zeros((1,2)) # inverse function = B^-1 *(x-b)\n",
    "inside_elem_node= np.zeros((128,2))\t\n",
    "X= np.zeros((128))\n",
    "Y= np.zeros((128))\t\n",
    "pert= .03 \t\t\t\t# a constant to be used to dislocate interpolation points \n",
    "\n",
    "# defining all the coordinates of the nodes\n",
    "for ii in xrange(n):\n",
    "\t\tfor jj in xrange(n):\n",
    "\t\t\t\tm[9*ii+jj][0]= x[jj]\n",
    "\t\t\t\tm[9*ii+jj][1]= y[ii]\n",
    "\n",
    "\n",
    "#print tri_connect(74,1)\n",
    "\n",
    "# B matrix for the first shape triangle \n",
    "B_odd = np.zeros((2,2))\n",
    "B_odd[:,0] = np.transpose([m[1][0]-m[0][0], m[1][1]-m[0][1]])\n",
    "B_odd[:,1] = np.transpose([m[9][0]-m[0][0], m[9][1]-m[0][1]])\n",
    "#print B_odd\n",
    "inv_B_odd= np.linalg.inv(B_odd)\n",
    "\n",
    "# B matrix for the second shape triangle \n",
    "B_even = np.zeros((2,2))\n",
    "B_even[:,0] = np.transpose([m[9][0]-m[10][0], m[9][1]-m[10][1]])\n",
    "B_even[:,1] = np.transpose([m[1][0]-m[10][0], m[1][1]-m[10][1]])\n",
    "inv_B_even= np.linalg.inv(B_even)\n",
    "print 'm = ',m[10][:], m[9][:], m[1][:]\n",
    "print inv_B_even\n",
    "\n",
    "\n",
    "for ii in range(0,128):\n",
    "    b[ii][:]= tri_connect(ii,0) # b values is [x1,y1] which changes for every triangle\n",
    " \n",
    "    x1=tri_connect(ii,0)\n",
    "    if ii<(n-1)*(n-1): \n",
    "        inside_elem_node[ii,0]= x1[0] + pert\n",
    "        inside_elem_node[ii,1]= x1[1] + pert\n",
    "        inverse_func= np.dot( inv_B_odd, ( np.subtract(inside_elem_node[ii][:], b[ii][:],) ) )  \n",
    "    else: \n",
    "        inside_elem_node[ii,0]= x1[0] - pert\n",
    "        inside_elem_node[ii,1]= x1[1] - pert\n",
    "        inverse_func= np.dot( inv_B_even, ( np.subtract(inside_elem_node[ii][:], b[ii][:],) ) )\n",
    "#    if ii==64:\n",
    "#        print inverse_func, inv_B_even, inv_B_odd, inside_elem_node[ii][:], b[ii][:], np.subtract(inside_elem_node[ii][:], b[ii][:],)\n",
    "    for jj in range(0,3):\n",
    "        z[jj][:]= tri_connect(ii,jj)\n",
    "        lag_glob[jj]= lagr_tri(jj,inverse_func[0],inverse_func[1])\n",
    "        #print ii, jj, inverse_func, lag_glob[jj], z[jj][:]\n",
    "\n",
    "\tlagr_poly[ii] = lag_glob[0]* calc_function(z[0][0],z[0][1]) + lag_glob[1]* calc_function(z[1][0],z[1][1]) + lag_glob[2]* calc_function(z[2][0],z[2][1])\n",
    "    if ii==36:\n",
    "        print calc_function(z[0][0],z[0][1]), calc_function(z[1][0],z[1][1]), calc_function(z[2][0],z[2][1])\n",
    "#print inside_elem_node\n",
    "#print lagr_poly\n",
    "#print inside_elem_node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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WjaH0xW2cPnwwXc2SP/20gj4DxxCd5wA4mFkoSATn+wPwr3SPrQFr06yV1XiR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\na+F/8X7gDwB22NhwbNQok9fYs20b5c3spNL8zfMIeLd49hTws7Rkc//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EU6dOsXvfHp4H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HyuZ/lq2sQXt/+D8AePSPSx/Aj8F9nyYEwxS2jUxqPtOpKSiTaMGDrM4u73Hz3A1d9yJatnuPp7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\nxZABA19a8Zoflixl5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e09b510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6VOo3ayTemX2lZKfqUub9elKifVXxyuQjzdu2lLNnz6ar3q5du6Rq3SDxzh4g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\nUu+PIfhPvU5K4uceX1qt4NmVSIN8KSkpTP5hDDsnfR4MPkYxF9g4Hn4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BXVA6p93YeGvN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Pk7ujsYow9ZLLJy9epVTp8+jTTtbfmYFRsh9m7odx96blfi8XM4Rj3hrbfeMnuIAwcOEJMYQ5HW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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7c9e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#################################\n",
    "# plotting the resutls\n",
    "#################################\n",
    "\n",
    "plt.figure(1)\n",
    "\n",
    "Z = np.zeros(128)\n",
    "for ii in range(128):\n",
    "\tZ[ii] = calc_function(inside_elem_node[ii,0],inside_elem_node[ii,1])\n",
    "\n",
    "plt.scatter(inside_elem_node[:,0],inside_elem_node[:,1], c=Z, s=150, alpha=1.0)\n",
    "plt.title('function values on the points within elements ',fontsize=12,color='black')\n",
    "\n",
    "plt.figure(2)\n",
    "plt.scatter(inside_elem_node[:,0], inside_elem_node[:,1], c=lagr_poly, s=150.0, alpha=1.0)\n",
    "plt.title('2d lagrange interpolation function values at element points ',fontsize=12,color='black')\n",
    "plt.show()\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  },
  "name": "HW2_Aslam.ipynb"
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
